High-precision analog in-memory computing

A memory circuit can calculate a weighted sum using currents. In an illustrative scaled example, inputs 3 and 4 with weights 2 and 1 should give 2 × 3 + 1 × 4 = 10. Voltages represent the inputs, and stored conductances—how readily each cell passes current—set the weights; the currents add. Real devices fluctuate or drift, so the answer can shift. Which combinations of error correction keep the answer accurate without spending away the energy saved by computing in memory?[1] [2]

Apply voltages to a resistive memory array and measure its output currents: ideally they represent a matrix–vector product, a set of weighted sums. For example, the illustrative scaled sum 2 × 3 + 1 × 4 equals 10. How should precision-recovery methods be combined when the physical output is imperfect, and which combinations retain an energy advantage after correction and conversion?

Conductance programming errors, drift, circuit noise and limited analog-to-digital resolution affect different stages. Slicing decomposes a weight or input into lower-precision parts, computes their contributions and recombines them with the appropriate scaling. This relaxes a single device’s precision requirement but adds work or hardware. For linear-equation solving, mixed-precision iterative refinement checks an approximate solution with a more accurate residual—the mismatch between the computed and required result—and uses a lower-precision solve to find a correction. Its convergence depends on the problem and error regime.

The June 2026 matrix-factorisation experiment uses two adjustable submatrices to represent the target calculation while bypassing faulty devices, achieving high accuracy and energy/density improvements in its evaluated benchmarks. The January review proposes systematic comparisons of combined methods, not the claim that high accuracy has never been achieved.[1] [2] [3]

One approach splits a precise number into easier, lower-precision parts and recombines their results. Other methods detect errors or repeatedly improve an approximate solution. Successful examples exist. Their combined accuracy and total energy still need comparison as input values, signal encoding and device noise change.[2] [3]

The interactions between modulation, input distributions, device/converter noise and correction algorithms still need characterisation for the stated multiplication and inverse-operation tasks. A complete comparison must include converters, extra resources and repeated correction steps as well as the array itself. A successful benchmark or one error regime does not establish the best combination across all workloads.[1] [2] [3]

A small arithmetic error can be tolerable for one task and unacceptable for another, such as solving a scientific model’s equations. Corrections and conversion between digital numbers and physical signals consume energy too. The useful choice depends on delivering the required answer accuracy at the cost of the whole computation.[1] [2]

Different numerical problems amplify hardware errors differently. The full error-and-cost relationship would identify when approximate physical arithmetic can be repaired economically and when a high-precision conventional computation is preferable. It would also make energy comparisons interpretable: the same answer tolerance and system boundary must be counted, rather than comparing an uncorrected array with a complete solver.[1] [2]